Detection of non-self-correcting nature of information cascade

We propose a method of detecting non-self-correcting information cascades in experiments in which subjects choose an option sequentially by observing the choices of previous subjects. The method uses the correlation function $C(t)$ between the first and the $t+1$-th subject's choices. $C(t)$ measures the strength of the domino effect, and the limit value $c\equiv \lim_{t\to \infty}C(t)$ determines whether the domino effect lasts forever $(c>0)$ or not $(c=0)$. The condition $c>0$ is an adequate condition for a non-self-correcting system, and the probability that the majority's choice remains wrong in the limit $t\to \infty$ is positive. We apply the method to data from two experiments in which $T$ subjects answered two-choice questions: (i) general knowledge questions ($T_{avg}=60$) and (ii) urn-choice questions ($T=63$). We find $c>0$ for difficult questions in (i) and all cases in (ii), and the systems are not self-correcting.